Perfect difference sets constructed from Sidon sets
Number Theory
2016-12-30 v1 Combinatorics
Abstract
A set A of positive integers is called a perfect difference set if every nonzero integer has an unique representation as the difference of two elements of A. We construct dense perfect difference sets from dense Sidon sets. As a consequence of this new approach, we prove that there exists a perfect difference set A such that A(x) >> x^{\sqrt{2}-1-o(1)}. We also prove that there exists a perfect difference set A such that limsup_{x\to \infty}A(x)/\sqrt x\geq 1/\sqrt 2.
Cite
@article{arxiv.math/0609244,
title = {Perfect difference sets constructed from Sidon sets},
author = {Javier Cilleruelo and Melvyn B. Nathanson},
journal= {arXiv preprint arXiv:math/0609244},
year = {2016}
}
Comments
11 pages, LaTex